Answer:
The width of the patio is 11.29 feet while the length of the patio is 13.29 feet
Step-by-step explanation:
Mathematically, the area of the patio can be calculated by multiplying the length by the breadth of the patio
Thus we have ;
(x + 7)(x + 9) = 150
x^2 + 7x + 9x + 63 = 150
x^2 + 16x + 63 = 150
x^2 + 16x + 63 -150 = 0
x^2 + 16x -87 = 0
we can use the quadratic formula to solve this completely
x = {-b ± √(b^2 - 4ac)}/2a
where a = 1, b = 16 and c = -87
Plugging the values we have
x = {-16 ± √(16^2 - 4(1)(-87)}/2
x = {-16 ± √(256+ 348)}/2
x = {-16 ± √(604}/2
x = (-16 + 24.58)/2 or (-16-24.58)/2
x = 4.29 or -20.29
Choosing x = -20.29 will make our dimensions negative, so we ignore it and make do with the positive value only
Thus our dimensions are 4.29 + 7 and 4.29 + 9
This is equal to 11.29 feet and 13.29 feet respectively
